e x ( 1 - cot x + cot 2 x ) ? d x =

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Solution

Q.
$\int e^{x} (1 - \cot x + \cot^{2} x) d x =$

1 $e^{x} \cot x + C$

2 $e^{x} cosec x + C$

3 $- e^{x} cosec x + C$

4 $- e^{x} \cot x + C$

Ans.
(4)

Ans. $- e^{x} \cot x + C$

Explanation :

$\int e^{x} (1 - \cot x + \cot^{2} x) d x$

   $= \int e^{x} (- \cot x + {cosec}^{2} x) d x$

$= e^{x} (- \cot x) + C$    $[∵ \int e^{x} {f (x) + f' (x)} d x = e^{x} f (x) + C]$

   $= - e^{x} \cot x + C$

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